The Magpies are reportedly happy to sell.
Thauvin's Magpies spell hasn't gone as planned
Marcelo Bielsa is set to be appointed Lazio manager this week, and the report claims the former Marseille chief is weighing up a reunion in Rome.
The pair previously worked together for a season at Stade Velodrome, where Thauvin was arguably at his best.
Bielsa is Lazio bound according to reports
The 23-year-old scored five goals and made eight assists during the 2014-15 campaign, as Bielsa delivered a fourth-placed finish for l'OM before resigning in August 2015.
And the report claims the Argentine feels he can get the best out of Thauvin, who's flopped following a £14 million move to Tyneside last summer.
The former France Under-21 international scored once and made two assists in 16 Magpies appearances, and spent the second half of the campaign back in Marseille on loan.
Moments like this were all too rare for Thauvin
The Ligue 1 side are said to be keen on another temporary deal for the former Bastia man, but Newcastle will consider all their options before allowing him to leave, the report claims.
The Magpies begin the new Championship season away at Fulham on Friday 5 August.